Diffraction - central spot covers moon

In summary, the problem asks for the diameter of a radar antenna that will cover the Moon with the central spot of its diffraction pattern. Using the formula for circular aperture, with a wavelength of 16.5cm and the distance from the Earth to the Moon at 4x10^8m, the calculated diameter is 50.325m. However, this may be incorrect and further clarification or a different formula may be needed.
  • #1
Ducks_in_OR
2
0

Homework Statement


The Moon is about 4x10^8 m from the Earth and has a diameter of about 3.2x10^6 m. You want a radar which just covers the Moon with the central spot of its diffraction pattern. If the radar has a wavelength of 16.5cm , what is the diameter of the radar antenna?

Homework Equations


Circular Aperture D=(2.44*λ*L)/(diameter of the moon)
D=diameter of the radar

The Attempt at a Solution


plugging in the values I found D=(2.44*(16.5*10^-2)*(4x10^8))/(3.2x10^6) and D=50.325m, which is incorrect. Am I making any incorrect assumptions, or is it the incorrect formula to be using for this type of problem.

Thanks
 
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  • #2
Can you tell me where the 2.44 comes from? Maybe a URL?
 
  • #3
no worries figured it out
 

Related to Diffraction - central spot covers moon

1. What is diffraction?

Diffraction is a phenomenon that occurs when light waves encounter an obstacle or slit that is comparable in size to the wavelength of the light. This causes the light to spread out and interfere with itself, producing a characteristic pattern of light and dark areas.

2. How does diffraction affect the central spot covering the moon?

The central spot covering the moon is a result of diffraction caused by the Earth's atmosphere. When light from the moon enters our atmosphere, it encounters various obstacles and particles, causing it to diffract and spread out. This results in the central spot we see covering the moon.

3. Why is the central spot covering the moon not always visible?

The visibility of the central spot covering the moon depends on various factors, such as the atmospheric conditions and the size of the particles in the atmosphere. If the atmosphere is clear and there are no large particles, the central spot may not be visible. However, if there are clouds or a lot of particles in the atmosphere, the central spot may be more pronounced.

4. Can diffraction be observed with other celestial bodies?

Yes, diffraction can be observed with other celestial bodies such as stars. However, the central spot covering the moon is the most commonly observed example of diffraction in the night sky due to its large size and proximity to the Earth.

5. How does the size of the central spot covering the moon change with distance?

The size of the central spot covering the moon does not change with distance. This is because the size of the central spot is determined by the size of the particles in the atmosphere and the wavelength of the light, which remain constant regardless of the distance between the observer and the moon.

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